Collaborative Research: Multiple Hypothesis Testing on the Regression Analysis

本研究项目将发展新的理论和方法，以解决回归分析下与错误发现率（FDR）控制有关的基本问题。将提供新的统计工具来分析来自各种科学研究的数据，如脑成像、全基因组关联研究和大气科学。分析复杂数据的统计方法的发展将有助于发现与血压、冠心病、中风和其他关键健康问题相关的关键变量。此外，该研究项目将为研究生提供培训机会，他们将获得技能，以满足工业界和学术界对数据科学家日益增长的需求，软件将被开发并在公众可访问的网站上提供。在回归分析的一般框架下，对高维数据进行多重测试分析是大数据时代的关键挑战。本项目将开发一个新的框架，用于执行回归分析的无模型多重测试，以及高维回归模型的最佳多重测试，以最大限度地检测受I型错误率控制的真实替代方案。当维数相对于样本量偏离时，该框架使统计推断能够进行足够的降维，并将当前关于多重测试的文献扩展到更复杂的数据结构，其中通常假设的模型假设无效。该框架还可以应用于可解释神经网络的推理。本研究项目不仅旨在推进多元检验理论的发展，而且着眼于已有理论的应用。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will develop new theories and methodologies for tackling fundamental issues related to false discovery rate (FDR) control under regression analysis. Novel statistical tools will be provided to analyze data from various scientific studies, such as brain imaging, genome-wide association studies, and atmospheric science. The development of statistical methods to analyze complex data will facilitate discoveries of key variables related to blood pressure, coronary heart disease, stroke, and other critical health issues. Furthermore, this research project will provide training opportunities for graduate students, who will acquire the skills to meet the growing demand for data scientists in industry and academia and software will be developed and made available on publicly accessible websites. Analyzing high-dimensional data using multiple testing under the general framework of regression analysis is a critical challenge in the era of big data. This project will develop a new framework for performing model-free multiple testing for regression analysis, as well as optimal multiple testing for high-dimensional regression model in terms of maximizing the power of detecting the true alternatives subject to the type I error rate control. This framework enables statistical inference for sufficient dimension reduction when the dimension diverges with respect to the sample size and expands the current literature on multiple testing to more complicated data structures where commonly assumed model assumptions are not valid. The framework could also be applied to draw inference for explainable neural networks. The research project not only aims to advance theories in multiple testing but also targets applications of the developed theories.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.